The bestselling author of Zero shows how mathematical misinformation pervades-and shapes-our daily lives.
According to MSNBC, having a child makes you stupid. You actually lose IQ points. Good Morning America has announced that natural blondes will be extinct within two hundred years. Pundits estimated that there were more than a million demonstrators at a tea party rally in Washington, D.C., even though roughly sixty thousand were there. Numbers have peculiar powers-they can disarm skeptics, befuddle journalists, and hoodwink the public into believing almost anything.
"Proofiness," as Charles Seife explains in this eye-opening book, is the art of using pure mathematics for impure ends, and he reminds readers that bad mathematics has a dark side. It is used to bring down beloved government officials and to appoint undeserving ones (both Democratic and Republican), to convict the innocent and acquit the guilty, to ruin our economy, and to fix the outcomes of future elections. This penetrating look at the intersection of math and society will appeal to readers of Freakonomics and the books of Malcolm Gladwell.
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Charles Seife is the author of five previous books, including Proofiness and Zero, which won the PEN/Martha Albrand Award for first nonfiction and was a New York Times notable book. He has written for a wide variety of publications, including The New York Times, Wired, New Scientist, Science, Scientific American, and The Economist. He is a professor of journalism at New York University and lives in New York City.
Excerpt. © Reprinted by permission. All rights reserved.:
Phony Facts, Phony Figures
Facts are stubborn things; and whatever may be our wishes, our inclinations, or the dictates of our passion, they cannot alter the state of facts and evidence.
Facts are stupid things.
If you want to get people to believe something really, really stupid, just stick a number on it. Even the silliest absurdities seem plausible the moment that they’re expressed in numerical terms.
Are blonds an endangered species? A few years ago, the media were all abuzz about a World Health Organization study proving that natural blonds would soon be a thing of the past. The BBC declared that people with blond hair “will become extinct by 2202.” Good Morning America told its viewers that natural blonds will “vanish from the face of the earth within two hundred years” because the blond gene is “not as strong a gene as brunettes’.” The story was winging its way around the globe until the WHO issued an unusual statement:
WHO wishes to clarify that it has never conducted research on this subject. Nor, to the best of its knowledge, has WHO issued a report predicting that natural blondes are likely to be extinct by 2202. WHO has no knowledge of how these news reports originated but would like to stress that we have no opinion on the future existence of blondes.
It should have been obvious that the story was bogus, even before the WHO denial. One geneticist had even told the BBC as much. “Genes don’t die out unless there is a disadvantage to having that gene,” he said. “They don’t disappear.” But the BBC had suspended its faculties of disbelief. The reason, in part, was because of a phony number. The specificity, the seeming mathematical certainty of the prediction of when the last blond would be born, gave the story an aura of plausibility. It suckered journalists who should have known better.
No matter how idiotic, how unbelievable an idea is, numbers can give it credibility. “Fifty-eight percent of all the exercise done in America is broadcast on television,” MSNBC host Deborah Norville declared in 2004, with a completely straight face. “For instance, of the 3.5 billion sit-ups done during 2003, two million, three hundred thousand [sic] of them were on exercise shows.” Without once pausing to think, Norville swallowed the bogus statistics and regurgitated them for her audience; just a moment’s reflection should have revealed that the story was nonsense. (A few months later, perhaps unwilling to be outdone by his colleague, MSNBC host Keith Olbermann touted “a five-year study just concluded at Indiana University” which proved that “upon the birth of their first child, 100 percent of parents lose at least 12 IQ points, and the average loss is 20.” These numbers, too, are fiction.) The numbers had short-circuited Norville’s brain, rendering her completely incapable of critical thought. It’s typical. Numbers have that power over us, because in its purest form, a number is truth.
The cold and crystalline world of numbers gives us the rarest of all things: absolute certainty. Two plus two is always four. It was always so, long before our species walked the earth, and it will be so long after the end of civilization.
But there are numbers and there are numbers. Pure numbers are the domain of mathematicians—curious people who study numbers in the abstract, as Platonic ideals that reveal a higher truth. To a mathematician, a number is interesting in its own right. Not so for the rest of us.
For a nonmathematician, numbers are interesting only when they give us information about the world. A number only takes on any significance in everyday life when it tells us how many pounds we’ve gained since last month or how many dollars it will cost to buy a sandwich or how many weeks are left before our taxes are due or how much money is left in our IRAs. We don’t care about the properties of the number five. Only when that number becomes attached to a unit—the “pounds” or “dollars” or “weeks” that signify what real-world property the number represents—does it become interesting to a nonmathematician.
A number without a unit is ethereal and abstract. With a unit, it acquires a meaning—but at the same time, it loses its purity. A number with a unit can no longer inhabit the Platonic realm of absolute truth; it becomes tainted with the uncertainties and imperfections of the real world. To mathematicians, numbers represent indisputable truths; to the rest of us, they come from inherently impure, imperfect measurements.
This uncertainty is unavoidable. Every unit represents an implied measurement. Inches, for example, represent an implied measurement of length; when someone says that a coffee table is eighteen inches wide, he’s saying that if we were to take the table and measure it with a ruler, the table would have the same length as eighteen of the little hash marks we call inches. When someone says he weighs 180 pounds, he’s saying that if you measured him with a bathroom scale, the number on the dial would read 180. Every number that has a real-world meaning is tied, at least implicitly, to a measurement of some kind. Liters are tied to a measurement of volume. Acres imply a measurement of area. Watts imply a measurement of power. A measurement of speed is expressed in miles per hour or in knots. A measurement of wealth is in dollars or euros or yuan. If someone says that he has five fingers, he’s saying that if you count his digits—and counting objects is a measurement too—the answer will be five fingers.
It’s universal; behind every real-world number, there’s a measurement. And because measurements are inherently error-prone (they’re performed by humans, after all, using instruments made by humans), they aren’t perfectly reliable. Even the simple act of counting objects is prone to error, as we shall see. As a result, every measurement and every real-world number is a little bit fuzzy, a little bit uncertain. It is an imperfect reflection of reality. A number is always impure: it is an admixture of truth, error, and uncertainty.
Proofiness has power over us because we’re blind to this impurity. Numbers, figures, and graphs all have an aura of perfection. They seem like absolute truth; they seem indisputable. But this is nothing but an illusion. The numbers of our everyday world—the numbers we care about—are flawed, and not just because measurements are imperfect. They can be changed and tinkered with, manipulated and spun and turned upside down. And because those lies are clad in the divine white garb of irrefutable fact, they are incredibly powerful. This is what makes proofiness so very dangerous.
It’s true: all measurements are imperfect. However, some are more imperfect than others. As a result, not all numbers are equally fallible. Some numbers, those that are based upon extremely reliable and objective measurements, can come very close to absolute truth. Others—based on unreliable or subjective or nonsensical measurements—come close to absolute falsehood. It’s not always obvious which are which.
Truthful numbers tend to come from good measurements. And a good measurement should be reproducible: repeat the measurement two or ten or five hundred times, you should get pretty much the same answer each time. A good measurement should also be objective. Even if different observers perform the measurement with different kinds of measuring devices, they should all agree about the outcome. A measurement of time or of length, for example, is objective and reproducible. If you hand stopwatches to a dozen people watching the same event—say, the Kentucky Derby— and ask them to time the race, they’ll all come up with roughly the same answer (if they’re competent). A whole stadium full of people, each using different stopwatches and clocks and time-measuring devices, would agree that the race took, say, roughly one minute and fifty-nine seconds to complete, give or take a few fractions of a second. Similarly, ask a dozen people to measure an object like a pencil, and it doesn’t matter whether they use a ruler or a tape measure or a laser to gauge its length. When they complete their measurements, they’ll all agree that the pencil is, say, four and a half inches long, give or take a fraction of an inch. The result of the measurement doesn’t depend on who’s doing the measuring or what kind of equipment’s being used—the answer is always roughly the same. This is an essential property of a good measurement.
Bad measurements, on the other hand, deceive us into believing a falsehood—sometimes by design. And there are lots of bad measurements. Luckily, there are warning signs that tell you when a measurement is rotten.
One red flag is when a measurement attempts to gauge something that’s ill-defined. For example, “intelligence” is a slippery concept—nobody can nail down precisely what it means—but that doesn’t stop people from trying to measure it. There’s an entire industry devoted to trying to pin numbers to people’s brains; dozens and dozens of tests purport to measure intelligence, intellectual ability, or aptitude. (An applicant to Mensa, the high-IQ society, has his choice of some thirty-odd exams to prove his intellectual superiority.) Testing is just the tip of the multimillion-dollar iceberg. After measuring your intelligence, some companies sell you a set of exercises that help you improve your score on their tests, “proving” that you’ve become smarter. Dubious claims are everywhere: video games, DVDs, tapes, and books promise to make you more intelligent—for a price. Even the British Broadcasting Company tried to cash in on the intelligence-enhancement fad. In 2006, a BBC program promised that you can become “40 percent cleverer within seven days” by following diet advice and doing a few brain-teasers. Was there a sudden surge in the number of Britons understanding quantum physics? Unlikely. So long as researchers argue about what intelligence is, much less how to measure it, you can be assured that the “40 percent cleverer” claim is worthless. In fact, I can personally guarantee that you’ll instantly be 63 percent smarter if you ignore all such statements.
Even if a phenomenon has a reasonable definition that everybody can agree about, it’s not always easy to measure that phenomenon. Sometimes there’s no settled-upon way to measure something reliably—there’s no measuring device or other mechanism that allows different observers to get the same numbers when trying to quantify the phenomenon—which is another sign that the measurement is dubious. For example, it’s hard to measure pain or happiness. There’s no such thing as a painometer or a happyscope that can give you a direct and repeatable reading about what a subject is feeling. (This doesn’t stop scientists from trying. To measure the effectiveness of painkillers in mice, some scientists use a calibrated hotplate; they measure pain by timing how long it takes for the mouse to jump or otherwise react to the hot surface.) In lieu of devices that can measure these experiences directly, researchers are forced to use crude and unreliable methods to try to get a handle on the degree of pain or happiness that a subject is feeling. They use questionnaires to gauge how much pain someone is in (circle the frowny face that corresponds with your level of pain) or how good someone feels (circle the number that represents how happy you are). Making matters even more difficult, pain and joy are subjective experiences. People feel them diff erently—some people are extremely tolerant to pain and some are very sensitive; some are emotional and regularly climb up towering peaks of bliss while others are more even-keeled. This means that even if a scientist could somehow devise an experiment where people would experience exactly the same amount of pain or joy, they would almost certainly give different answers on the questionnaire because their perceptions are different. A swift kick to the shins will elicit a super-duper frowny face from someone who has a low pain tolerance, while a more stoic person would barely deviate from a mild grimace. When rational people will come up with different answers to a question—how painful a blow to the head is, how beautiful a person in a photo is, how easy a book is to read, how good a movie is—the measurement can have some value, but the number is certainly far from the realm of absolute truth.
But it’s not the farthest away. That honor goes to numbers that are tied to phony measurements—measurements that are fake or meaningless or even nonexistent. Numbers like these are everywhere, but product labels seem to be their favorite habitat. Just try to imagine what kind of measurement L’Oreal made to determine that its Extra Volume Collagen Mascara gives lashes “twelve times more impact.” (Perhaps they had someone blink and listened to how much noise her eyelashes made when they clunked together.) How much diligence do you think Vaseline put into its research that allowed it to conclude its new moisturizer “delivers 70 percent more moisture in every drop.” (Presumably it would deliver less moisture than water, which is 100 percent moisture, after all.) No matter how ridiculous an idea, putting it into numerical form makes it sound respectable, even if the implied measurement is transparently absurd. This is why paranormal researchers feel compelled to claim, without giggling, that 29 percent of Christian saints had exhibited psychic powers.
Making up scientific-sounding measurements is a grand old tradition; cigarette companies used to excel at the practice, the better to fill their ads with a thick haze of nonsense. “From first puff to last, Chesterfield gives you a smoke measurably smoother . . . cooler . . . best for you!” read one advertisement from 1955. You can’t measure the smoothness and coolness of a cigarette any more than you can measure the impact of an eyelash. Even if people tried to quantify impact or smoothness or coolness, the results would be worthless. These are phony measurements. They’re like actors dressed up in lab coats—they appear to be scientific, but they’re fake through and through. As a result, the numbers associated with these measurements are utterly devoid of meaning. They are fabricated statistics: Potemkin numbers.
According to legend, Prince Grigory Potemkin didn’t want the empress of Russia to know that a region in the Crimea was a barren wasteland. Potemkin felt he had to convince the empress that the area was thriving and full of life, so he constructed elaborate façades along her route—crudely painted wooden frameworks meant to look like villages and towns from afar. Even though these “Potemkin villages” were completely empty—a closer inspection would reveal them to be mere imitations of villages rather than real ones— they were good enough to fool the empress, who breezed by them without alighting from her carriage.
Potemkin numbers are the mathematical equivalent of Potemkin villages. They’re numerical façades that look like real data. Meaningful real-world numbers are tied to a reasonably solid measurement of some sort, at least implicitly. Potemkin numbers aren’t meaningful because either they are born out of a nonsensical measurement or they’re not tied to a genuine measurement at all, springi...
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